Short Note
Version 1
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A Determinantal Expression and a Recurrence Relation for the Euler Polynomials
Version 1
: Received: 11 October 2016 / Approved: 11 October 2016 / Online: 11 October 2016 (10:40:02 CEST)
How to cite: Qi, F.; Guo, B.-N. A Determinantal Expression and a Recurrence Relation for the Euler Polynomials. Preprints 2016, 2016100034. https://doi.org/10.20944/preprints201610.0034.v1 Qi, F.; Guo, B.-N. A Determinantal Expression and a Recurrence Relation for the Euler Polynomials. Preprints 2016, 2016100034. https://doi.org/10.20944/preprints201610.0034.v1
Abstract
In the paper, by a very simple approach, the author establishes an expression in terms of a lower Hessenberg determinant for the Euler polynomials. By the determinantal expression, the author finds a recurrence relation for the Euler polynomials. By the way, the author derives the corresponding expression and recurrence relation for the Euler numbers.
Keywords
determinantal expression; recurrence relation; Euler polynomial; Euler number; Hessenberg determinant
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (3)
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Commenter: kader
The commenter has declared there is no conflict of interests.
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the corresponding author of this paper.
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author for this preprint
Feng Qi and Bai-Ni Guo, A determinantal expression and a recurrence relation for the Euler polynomials, Advances and Applications in Mathematical Sciences 16 (2017), no. 9, 297--309.